Quantifying isotopic heterogeneity of candidate reference materials at the picogram sampling scale

We propose a method for quantifying the in situ heterogeneity of solid materials at the picogram test portion scale, illustrating its use by investigating the oxygen isotope ratio (18O-/16O-) of four quartz samples. Using Secondary Ion Mass Spectrometry we could estimate the intrinsic heterogeneity using a large number (~100) of closely-spaced duplicated measurements. An analysis of variance was then applied to these large data sets to extract the measurement repeatability (typically 0.10 - 0.15‰, 1s) from the total variability, thereby revealing a variability ranging from 0.18 ‰ to 2.3 ‰ which can be attributed to the genuine isotope ratio heterogeneities. A small proportion of outlying values were either rejected manually after inspection, or were accommodated using robust statistics. We also evaluated two distinct approaches for estimating and correcting instrumental drift; the use of a sub-area of the test material (if shown to have sufficiently low heterogeneity) is judged to be preferable to using a piece of unrelated silicate glass which we believe to be homogeneous. We also compared three approaches for estimating measurement repeatability, from which we show that the ‘duplicate method’ applied to the reference material is preferable to using other methods based either on the drift monitoring material or on assessing residuals of the drift monitoring material after drift correction. Finally, here we propose a strategy for predicting the number of measurements on individual fragments of a material that would be required to achieve a specified target uncertainty

Zum Problem repräsentativer Querschnitte von kleinen Teilgruppen der Bevölkerung am Beispiel des Projekts "Lebensverläufe und Wohlfahrtsentwicklung"

In dem Forschungsprojekt 'Lebensverläufe und Wohlfahrtsentwicklung' des SFB 3 der Universität Mannheim sollen die Lebensläufe von Männern und Frauen sozialhistorisch unterschiedlich verorteter Geburtskohorten nach mehreren Dimensionen untersucht werden. Methodisch stellt sich im Vorfeld der Datenerhebung das Problem eines sowohl systematischen als auch ökonomisch noch realisierbaren Stichprobenverfahrens. Aufgabe war die Erstellung einer Sticprobe von Personen deutscher Staatsangehörigkeit aus drei Geburtsjahrgängen, wobei die Stichprobe für jeden der beteiligten Jahrgänge repräsentativ angelegt werden mußte. Es kann gezeigt werden, daß der Stichprobenplan, der vom Arbeitskreis Deutscher Marktforschungsinstitute entwickelt worden ist, auch für repräsentative Querschnitte relativ kleiner Teilpopulationen herangezogen werden kann. Der Vergleich der durch die Adressenvorerhebung gewonnenen Stichprobe mit den Daten des Mikrozensus 1978 zeigt die Güte des Verfahrens. Dennoch dürfen die grundsätzlichen Probleme dieses Verfahrens nicht als erledigt betrachtet werden. Die Konsequenz ist die Prüfung und Erprobung alternativer Stichprobenpläne. (GB

U-Pb dating of zircons by ion microprobe : case studies from the Northwestern Yilgarn Craton, Western Australia

This thesis has two principle objectives: to provide geochronological data for the Late Archean Murchison Province of Western Australia and to assess the strengths and limitations of the ion microprobe zircon dating technique. A project was conducted to provide zircon U/Pb age measurements on seven granitoid samples from the Murchison granite-greenstone terrain. These data represent the first systematic U/Pb age survey for the granitoids from this 100,000 km2 region. The oldest sample found in region was from a pegmatite-banded gneiss which contained a complex zircon population, the best estimate for the emplacement age for the magmatic precursor is circa 2919 ± 12 Ma (1cr). Two samples of recrystallized monzogranite, by far the dominant lithology in the region, gave emplacement ages of 2704 ± 51 and 2681 ± 6 Ma. Two samples from the southern post-folding granitoid suite gave ages of 2641 ± 5 and 2602 ± 14 Ma. Two samples collected from a pluton previously assigned to the northern post-folding granitoid suite gave ages of 2760 ± 8 and 2784 ± 22 Ma; this pluton has now been reinterpreted as a heretofore unrecognized synvolcanic suite which may be coeval with the nearby Mount Farmer greenstones. In addition to providing the first zircon age determinations for the major granitoid units in the area, these data also constrain the eruption ages of the two greenstone sequences and the timing of the regional deformation and metamorphic events. The absence of mid-Archean or older xenocrysts implies that the central Murchison Province is solely a product of Late Archean crustal growth. The success of this project was closely linked to the availability of a detailed tectonic model based on extensive field mapping by the Geological Survey of Western Australia. During this survey of the Murchison Province a unique sample was encountered which gave unusually reversely discordant U/Pb systematics. An extensive investigation of this phenomena revealed the presence of a well-mixed, highly radiogenic Pb which apparently entered the zircon population at circa 0 Ma. Based on isotope dilution data, it appears that the sputtering characteristics of this external component deviated significantly from the calibration standard which was used to determine the ion microprobes U/Pb discrimination factor. A second field-oriented project was conducted at Poona Rock, a typical outcrop of the 3500 km2 Murgoo Gneisses located along the western margin of the Murchison Province. Ion microprobe zircon analyses of six samples from this isolated outcrop all gave Late Archean emplacement ages. Because of the rapid evolution of Poona Rock, these data provided a rare opportunity to define precisely the age of the deformation which is seen on both the local and regional scales. This led to an extensive investigation of the accuracy and precision of the ion microprobe method. It was discovered that the ages calculated could be significantly affected by the assumptions made during the data assessment process. In complex data sets, the use of error estimates based on Poisson ion counting resulted in certain samples being designated as outliers which, when using more generous error assignments based on observed internal reproducibilities, apparently were part of the magmatic population. The complex U/Pb systematics observed in the samples were further attested to by the zircon structures and morphologies seen in these six samples. All analyses reported here were tested for excess internal error in their Pb/Pb ratios. The seven scans of the mass spectrum were compared to a mixing line joining the mean of the seven scans and an assumed common Pb end-member. In many cases it was found that the observed scatter of the data away from this mixing line was greater than that predicted by the best-possible-limit imposed by the observed ion count rates. A further refinement to the data assessment was the introduction of a best-fit plane technique for calculating the concordia intercept ages of a pool of data. This method has two advantages over data assessment based on the mean 207PbJ206pb ratio: this 3-dimensional approach requires neither an assumed common Pb composition nor an assumed 0 Ma lower concordia intercept. Despite these advantages, the best-fit plane method is unable to define a magmatic age when a population contains numerous measurements which diverge only slightly from the main population. Finally, an assessment of the 312 measurements conducted on the SL3 standard showed the presence of a previously unrecognized and significant fractionation of the Pb isotopic spectrum. The magnitude of the ion microprobe's fractionation is estimated at between 3 and 5%o per mass unit. This conclusion is directly dependent on the 572 Ma age which has been assigned to the SL3 standard

Klassifikation mit Clusteranalyse: grundlegende Techniken hierarchischer und K-means-Verfahren

'Nach einer Einführung in die Ziele der Clusteranalyse werden die Grundprinzipien der Algorithmen hierarchisch-agglomerativer und K-means-Verfahren dargestellt. Ein Schwerpunkt liegt auf der graphischen Darstellung der Ergebnisse. Außerdem werden einige Verfahren zur Validierung von Clusterlösungen, wie der Vergleich von Lösungen hierarchisch-agglomerativer Verfahren mit K-means-Lösungen sowie Monte-Carlo-Verfahren zur Exploration des Einflusses von Startbedingungen bei K-means-Verfahren, vorgestellt.' (Autorenreferat)'The paper presents a short introduction to the aims of cluster analysis and describes the principles of hierarchical-agglomerative and K-means procedures. Graphical representations play an important role, while validation, for example by comparison of different hierarchical and K-means solutions or by Monte-Carlo simulations, is an important issue.' (author's abstract)

Singuläre und multiple Imputation fehlender Einkommenswerte: ein empirischer Vergleich

'Die Messung des Haushaltseinkommens ist besonders stark vom Problem des item-nonresponse betroffen. So beträgt der Anteil der fehlenden Werte im ALLBUS 1996 trotz Nachfrage mit Einkommenskategorien 26 (Westdeutschland) bzw. 19 Prozent (Ostdeutschland). Beim Eurobarometer 1992 liegt der Ausfall zwischen 6 und fast 50 Prozent. In der Forschungspraxis wird der Datenausfall oft entweder ignoriert oder durch einfache Imputationen, d.h. durch Zuweisung von Mittelwerten korrigiert. Diese Vorgehensweisen werden von Rubin (1987) in Frage gestellt, der statt dessen eine multiple Imputation befürwortet. Mit dieser Methode werden die fehlenden Werte mehrfach rekonstruiert, wobei jedesmal die Unsicherheit der auf einer Regressionsgleichung basierenden Einkommenschätzung berücksichtigt wird. Das vorliegende Papier untersucht am Beispiel der Eurobarometerdaten von 1992, welche Folgen eine einfache versus multiple Rekonstruktion der fehlenden Einkommenswerte für die Schätzung des Einkommenseffektes auf die Lebenszufriedenheit hat.' (Autorenreferat)'Income measurement is plagued by the problem of item nonresponse. For example, in the 1996 ALLBUS survey 26 percent of the sample in western Germany and 19 percent of the sample in eastern Germany have missing data on income. In Eurobarometer 1992 the percentage of missing data on income ranges between 6 and 5O percent across countries. Research using income as an explanatory variable usually ignores this problem or tries to solve it by replacing missing values by some form of means estimation. This procedure, called simple imputation, differs from the multiple imputation proposed by Rubin (1987). In multiple imputation, holes in the data are also filled by regression estimated means. The procedure is repeated several times, taking into account the regression error each time. Using Eurobarometer 1992 data, the paper compares the consequences of using simple imputation versus multiple imputations to estimate the effect of income on life satisfaction ratings.' (author's abstract)

Methodenbericht: Allgemeine Bevölkerungsumfrage der Sozialwissenschaften: ALLBUS 1986

Ziel des Forschungsprogramms 'Allgemeine Bevölkerungsumfrage der Sozialwissenschaften' (ALLBUS) ist die Generierung und Bereitstellung von Daten für die empirische Sozialforschung. Die regelmässige Erfassung von Informationen und Einstellungen, Werthaltungen und die demographische Struktur der Bevölkerung der Bundesrepublik Deutschland schafft eine kontinuierliche, inhaltlich fruchtbare und methodisch anspruchsvolle Datengrundlage für sekundäranalytische Forschungsvorhaben. Der Methodenbericht zum ALLBUS 1986 enthält: (1) Informationen zur Vorbereitung des Frageprogramms und der begleitenden Methodenstudie; (2) Beschreibung der Durchführung und der Ergebnisse des Pretests; (3) Besonderheiten der Hauptstudie (Grundgesamtheit, Stichprobe, Feldphase; Ausschöpfung; Interviewsituation); (4) Beschreibung der Gewichtung der erhobenen Variablen sowie (5) Begründung des Wechsels des Datenerhebungsinstitutes. Darüber hinaus wird die MEthodenstudie zum ALLBUS 1986 dargestellt, die als 'Non-Response-Studie' den Problembereich sinkender Ausschöpfungsquoten für sozialwissenschaftliche Umfragen und die damit verbundenen Konsequenzen näher beleuchten soll. (HN